论文标题
关于高斯过程回归无法最佳学习组成功能
On the inability of Gaussian process regression to optimally learn compositional functions
论文作者
论文摘要
我们严格地证明，如果目标函数具有组成结构，那么深层过程先验可以超越高斯工艺先验。为此，我们研究了连续回归模型中高斯过程回归后收缩率的信息理论下限。我们表明，如果True函数是通用的加性函数，那么基于任何平均零高斯过程的后验只能以严格慢的速率恢复真相，而该速率比最小值速率慢了，而最小值速率是样本尺寸$ n $的多项式次优的因素。
We rigorously prove that deep Gaussian process priors can outperform Gaussian process priors if the target function has a compositional structure. To this end, we study information-theoretic lower bounds for posterior contraction rates for Gaussian process regression in a continuous regression model. We show that if the true function is a generalized additive function, then the posterior based on any mean-zero Gaussian process can only recover the truth at a rate that is strictly slower than the minimax rate by a factor that is polynomially suboptimal in the sample size $n$.
